Quantum Chemical Descriptors in Computational Medicinal Chemistry for Chemoinformatics

1. Quantum Chemical Descriptors in Computational Medicinal Chemistry for Chemoinformatics V. Subramanian Chemical Laboratory Central Leather Research Institute Chennai 600 020

2. Schematics Introduction to Informatics Molecular Models QSAR Descriptors for QSAR Conceptual DFT DFT based Reactivity Descriptors Applications Summary

4. IT for managing chemical information and solving chemical problems Chemistry + information science + computer science Driven by drug discovery research Chemoinformatics

5. Chemoinformatics Chemoinformatics is the amalgamation of those chemical information resources to transform data into vital information and chemical information into knowledge for the intended purpose of making better decisions faster in the area of drug lead identification and organization

7. Combinatorial chemistry Synthesizing large numbers of related chemical compounds Can help design drug leads Information rich Physiology of the biological effect Starting material properties Synthesis protocols

9. Drug discovery

10. Related Aspects Bioinformatics and chemoinformatics are generic terms that encompass the design, creation, organization, management, retrieval, analysis, dissemination, visualization and use of chemical and biological information

11. Chemometrics strategies

15. Locality of the model

16. QSAR The quantitative structure- activity relationship (QSAR) and the quantitative structure- property relationship (QSPR) are the important tools of the bio-chemo-informatics which can be built essentially based on the data generated from the molecular modeling and computational chemistry

17. QSAR Quantitative Structure Activity Relationship is a set of methods that tries to find a mathematical relationship between a set of descriptors of molecules and their activity. The descriptors can be experimentally or computationally derived. Using regression analysis, one can extract a mathematical relationship between chemical descriptors and activity.

18. QSAR Postulates the molecular structure is responsible for all the activities Similar compounds have similar biological and chemico-physical properties (Meyer 1899) Hansch postulate (1963) biological system + compound = f1(Lipolificity) + f2(Electronics) + f3(Steric) + f4(Molecular-prop) Congenericity postulate QSAR is applicable only to similar compounds

19. Descriptors in QSAR study Constitutional Descriptors Topological Descriptors Geometrical Descriptors Electrostatic Descriptors Quantum Chemical Descriptors MO Related Descriptors Thermodynamic Descriptors DFT based Reactivity Descriptors

20. Constitutional Descriptors  Total number of atoms in the molecule Absolute and relative numbers of atoms of certain chemical identity (C, H, O, N, F, etc.) in the molecule Absolute and relative numbers of certain chemical groups and functionalities in the molecule Total number of bonds in the molecule Absolute and relative numbers of single, double, triple, aromatic or other bonds in the molecule Total number of rings, number of rings divided by the total number of atoms Total and relative number of 6 membered aromatic rings Molecular weight and average atomic weight

21. Topological Descriptors Wiener index Randi's molecular connectivity index Randi indices of different orders Balaban's J index Kier and Hall valence connectivity indices Kier shape indices Kier flexibility index Mean information content index Structural information content index Complementary information content index Bonding information content index Topological electronic indices

23. Geometrical Descriptors Molecular surface area Solvent-accessible molecular surface area Molecular volume Solvent-excluded molecular volume Gravitational indexes Principal moments of inertia of a molecule Shadow areas of a molecule Relative shadow areas of a molecule

24. Electrostatic Descriptors Gasteiger-Marsili empirical atomic partial charges Zefirov's empirical atomic partial charges Mulliken atomic partial charges Minimum (most negative) and maximum (most positive) atomic partial charges Polarity parameters Dipole moment Molecular polarizability Molecular hyperpolarizability Average ionization energy Minimum electrostatic potential at the molecular surface Maximum electrostatic potential at the molecular surface Local polarity of molecule Total variance of the surface electrostatic potential Electrostatic balance parameter

25. Quantum Chemical Descriptors Total energy of the molecule Total electronic energy of the molecule Standard heat of formation Electron-electron repulsion energy for a given atomic species Nuclear-electron attraction energy for a given atomic species Electron-electron repulsion between two given atoms Nuclear-electron attraction energy between two given atoms Nuclear repulsion energy between two given atoms Electronic exchange energy between two given atoms Resonance energy between given two atomic species Total electrostatic interaction energy between two given atomic species Total interaction energy between two given two atomic species Total molecular one-center electron-electron repulsion energy Total molecular one-center electron-nuclear attraction energy Total intramolecular electrostatic interaction energy Electron kinetic energy density Energy of protonation 21

30. MO Related Descriptors Highest Occupied Molecular Orbital (HOMO) energy Lowest Unoccupied Molecular Orbital (LUMO) energy Absolute hardness Activation hardness Fukui atomic nucleophilic reactivity index Fukui atomic electrophilic reactivity index Fukui atomic one-electron reactivity index Mulliken bond orders Free valence

31. Thermodynamic Descriptors Vibrational enthalpy of the molecule Translational enthalpy of the molecule Vibrational entropy of the molecule Rotational entropy of the molecule Translational entropy of the molecule Vibrational heat capacity of the molecule Normal coordinate eigen values (EVA)

32. Density Functional Theory (DFT) Instead of calculating a wavefunction, tries to calculate the exact density of the molecule Based on the Hohenberg-Kohn proof, which stipulates that a given density corresponds to a particular wavefunction and potential Calculate the exact density ? obtain the exact wavefunction from the exact density ? Do everything you�d normally do with a MO wavefunction

33. DFT Evolution Thomas-Fermi Theory (1926-28)- established the direct mapping between electron density and potential. Landau Theory of Fermi liquids(1956-58) - introduced the energy of the system as a functional of charge distribution. Hohenberg-Kohn-Shem Theory (1964-65) - proved one-to-one mapping of the density and potential. Derived the equations for single electron wave functions, which can be solved in a mode of self-consistent-field. Talman-Shadwick Theory (1976) and Its Krieger-Li-Iafrate approximation (1992) - exact expression for exchange potential.

51. Polychlorinated biphenyls

52. Optimized Structures of PCBs

53. Analysis of PCBs The geometry of 22'55'- TCBP and 33`44`5- PCBP were optimized by using Becke�s three parameter hybrid density functional, B3LYP/6-31G*, which includes both Hartree-Fock exchange and DFT exchange correlation functionals. Above calculations are carried out using the GAUSSIAN 98 package. The optimized geometries were characterized by harmonic vibrational frequencies which confirmed that the structure of 22'55'- TCBP is a minimum on the potential energy surface.

54. Table 1: Calculated Relative Energy, Chemical Hardness, Chemical Potential, Polarizability, and Electrophilicity Index of 2,2�,5,5�-TCBP

55. Figure 1: The variation of relative energy (kJ/mol), chemical hardness (eV) and scaled hardness (eV) with the torsional angle (degrees) for 33'44'5 - PCBP.

56. Analysis of PCBs To select proper electronic descriptor based on DFT, for the possible toxicity of the 22'55'- TCBP, the various reactivity and selectivity descriptors such as chemical hardness, chemical potential, polarizability, electrophilicity index and the local electrophilic power are calculated for all the rotated conformations (Table 1). It has been found that 22`55`- TCBP has very large rotational energy barrier at ?=0? and ?=180? with relative energy of 53.17 kJ/mol. Due to large rotational barrier, this molecule cannot adapt planar conformation and hence it is less toxic.

57. Analysis of PCBs In the case of 33`44`5- PCBP with very small rotational energy barrier of 7.36 kJ/mol at the planar orientation (Figure 1), is shown to have flexible planarity so that it changes its conformation while moving in biological systems, thereby interacting readily, exhibiting its toxic properties.

58. The electron accepting nature of PCB is evident from the charge transfer calculation.

60. Optimized geometry of Benzidine

61. Benzidine

63. Benzidine

64. Table 2:Calculated Global Parameters for Benzidine

65. Analysis of Benzidine The relative energy of benzidine is calculated as a function of torsional angle , (rotation through the C (atom No.7)-C (atom No. 3) bond). To calculate the relative energy, the geometry at various values were optimized at B3LYP/6-31G* level.

66. Analysis of Benzidine It is possible to note from the rotational energy barrier (Table 2), which has a small variation (0 to 11.19 kJ/mol) that this molecule is highly flexible and it can adopt variety of conformations. This rotational freedom allows benzidine to freely interact with the cellular components in the realistic environment and hence their toxic nature.

67. The molecular electrostatic potential surfaces for various conformation of Benzidine.

69. MESP for Benzidine The MESP surface of benzidine reveals the site of attack and also provides clues for the role of electrostatic interactions involved in the reactivity. Further the charge transfer between benzidine and nucleic acid bases/base pairs, AHH receptors has clearly revealed the electron donating nature of benzidine.

72. Testosterone and Estrogen Derivatives

73. Structure of Testosterone and Estrogen

74. Table 3: Electrophilicity index of testosterone derivatives with their observed and calculated biological activity in terms of relative binding affinity (RBA)

75. Table 4: Electrophilicity index of 16?-substituted estradiol derivatives with their observed and calculated biological activity

76. Relationship between various biological activity of Testosterone derivatives and Electrophilicity index

77. Relationship between RBA valuesof Estrogen derivatives and Electrophilicity index

78. QSAR analysis of testosterone and estrogen derivatives The biological activity of testosterone and estrogen derivatives has been analyzed by our group using electrophilicity index as a descriptor. In this context, the SAR based on electrophilicity has been shown to be promising.

79. QSAR analysis of testosterone and estrogen derivatives Since the electrophilicity index is a chemical reactivity descriptor and its definition has strong foundation from the density functional theory, it is appropriate to make use of this descriptor in the QSAR parlance and the usefulness of such application was evident from our investigation. Results emanated from that study (above Tables and Figures) showed that the electrophilicity can be used as a descriptor of biological activity and it is quite interesting that a single descriptor can provide such a beautiful correlation.

80. Group Philicity

81. Group Philicity

83. Reactivity trends using Philicity Group philicity values derived from both MPA and HPA schemes have provided the expected reactivity trends in all sets of molecules considered for evaluation. Hence philicity and group philicity can be used as better chemical reactivity descriptors when compared to all other local reactivity descriptors.

84. QSAR studies on Alkanes (C2-C8)

85. Table 6: Abbreviations of the selected alkanes and their isomers (C2-C8)

86. Table 7: Regression equations and statistical parameters of the six quantum chemical descriptors for the five macroscopic properties

88. QSAR/QSPR analysis on Alkanes (C2-C8) The present study reveals that ionisation potential can be used as a descriptor to understand structure activity and structure property relationship. Within the framework of Hartree-Fock theory, the computed IP has excellent correlation with the macroscopic properties such as boiling point, heat of formation or enthalpy, entropy, heat capacity and heat of vaporisation. The correlation coefficient has been found to be high for the relationship between I and BP.

89. QSAR/QSPR analysis on Alkanes (C2-C8) Hardness and softness indices exhibit similar correlation coefficient in the range of 0.80-0.95 for all the macroscopic properties, which confirms the fact that both the microscopic properties are interrelated. Maximum correlation coefficient for both the indices has been found to be 0.945 for heat of formation. This observation reinforces the existing fact that, hardness (?) holds direct relationship with the stability of a molecule.

90. Summary The success of DFT based global and local quantum chemical descriptors in predicting the Chemo and Bio-activities of several systems selected by our group are highlighted in this work. The simple calculation procedure and the usefulness of all DFT based descriptors in the QSAR and QSPR parlance have also been probed in detail. In this study, the applications of global and local descriptors in the development of QSAR and QSPR have been presented for prediction of physical properties of series of alkanes, biological activity of testosterone and estrogen derivatives and toxicity of polychlorinated biphenyls, and benzidines.

91. Summary It has been shown that the global descriptors such as electrophilicity and ionization potential are capable of predicting the biological activity of the selected molecules Local descriptors such as philicity and group philicity are capable of identifying the activity of a particular site in the molecule and also in analyzing its toxicity as well as its behavior during an intermolecular reaction.

92. Acknowledgements T. Ramasami P. K. Chattaraj R. Parthasarathi J. Padmanabhan M. Elango DST and CSIR for funding